Formal Verification of the Empty Hexagon Number · HackerPapers discussions

Formal Verification of the Empty Hexagon Number — mentioned by bsubs

Sun, 16 Aug 2026 18:35:39 GMT

Hi! One of the authors here. Whether checking the LLM-generated Lean statements/definitions is easy or not depends heavily on the area of mathematics and the concrete definitions at play. In this case it was remarkably easy. As you can see in the repository, the definition of a countermodel is easy to parse, and the statement corresponding to their nonexistence for n <= 11 is also very easy to check. If you have any questions regarding them, I would be happy to answer them. Personally, this is one of the cases with LLM-generated Lean that I feel most comfortable with: the proofs are all…

Paper and discussion history. A mention is not an endorsement.

Formal Verification of the Empty Hexagon Number — mentioned by dwrensha

Fri, 29 Aug 2025 12:00:37 GMT

> David Renshaw recently gave a formal proof in Lean that the triakis tetrahedron does have Rupert's property That's me! This result appears to be significantly harder to formalize. Steininger and Yurkevich's proof certificate is a 2.5GB tree that partitions the state space into 18 million cells and takes 30 hours to validate in SageMath. Formalizing the various helper lemmas in the paper does seem achievable to me, but I suspect that applying them to all of the millions of cells as part of a single Lean theorem could present some significant engineering difficulties. I think it'd be a fun…

Paper and discussion history. A mention is not an endorsement.